2nd GENERATION DOT-OFF-DOT STOCHASTIC HALFTONE

ABSTRACT

As set forth herein, computer-implemented methods and systems facilitate employing a single stochastic screen defined up to a specified transition level. The dots at the specified level are connected to form a triangle tessellation with an associated spot function. For up to three colorants, a vector screening technique is employed, which involves a first colorant dot being grown from the vertices, second colorant dot grown from the triangle center, and a third colorant dot grown from the side midpoints. Growth in this manner ensures separation of colorants up to a certain density level. In cases where fourth colorant is to be used at a given pixel, the fourth colorant can be added using methods typically used for clustered screens, such as stochastic screening of the lightest colorant, in order to mitigate color shift sensitivity issues.

TECHNICAL FIELD

The presently disclosed embodiments are directed toward methods and systems for printing, reproducing or displaying images. More particularly, the teachings disclosed herein are applicable to methods and apparatuses wherein clustered-dot halftoning is implemented.

BACKGROUND

Digital images may be formatted as contone (continuous tone) images having a wide range of tonal values or may be formatted as coarsely quantized images having a limited number of tonal values, such as two levels for a binary image. Digital halftoning is a process of transforming a contone image to a coarsely quantized image. Digital halftoning is an important step in printing or displaying digital images possessing contone color tones because most printing processes are operating in a binary mode. Examples of such marking processes are offset printing presses, xerography, and ink-jet printing. In these processes, for each color separation of an image, a corresponding colorant spot is either printed or not printed at any specified image location, or pixel. Digital halftoning controls the printing of color dots formed by combinations of colorant spots of a colorant set, where the spatial averaging of the printed colorant dots, such as by the human visual system, provides the illusion of the required continuous tones.

Digital images and the resulting prints are formed of one or more colorant separations, also referred to as “color separations.” A monochrome image is formed of one colorant separation, typically black. Process color images are typically constructed of cyan, magenta, yellow, and black separations. Duotone and tritone images are formed of two and three separations, respectively. Spot color images have multiple colorant separations, where at least one colorant is positioned spatially non-overlapping with other colorants. Extended colorant set images typically include the process-color colorant separations plus one or more additional colorant separations such as green, orange, violet, red, blue, white, varnish, light cyan, light magenta, gray, dark yellow, metallics, and so forth. In the present teachings, we will use the terms “color images”, “color dots”, “color spots”, “colorant” and similar language to refer to images and marking systems with any number of colorants. The teachings herein apply particularly to any individual color separation of a digital image and resulting print, where that digital image or print can be composed of one or more separations. With the advent of computers, it is desirable for graphic artists and others to manipulate contone images and print them as halftone images. However, typical computer printers and typesetters are incapable of printing individual halftone dots in an infinite number of sizes. Instead, each halftone dot of a printed picture is in turn comprised of a collection of discrete, smaller “spots” or “pixels”, which are generally the smallest marks a printer or typesetter can make.

A common halftone technique is called screening, which compares the required continuous color tone level of each pixel for each color separation with one or more predetermined threshold levels. The predetermined threshold levels are typically defined for halftone cells that are tiled to fill the plane of an image, thereby forming a halftone screen of threshold values. At a given pixel, if the required color tone level is greater than the halftone threshold level for that pixel, a “1” is generated in the halftone output, so that a colorant spot is printed at that specified pixel in the subsequent printing operation. If the required color tone at a given pixel is less than the halftone threshold level for that pixel, a “0” is generated in the halftone output, so that a colorant spot is not printed at that specified pixel in the subsequent printing operation. The output of the screening process is a binary pattern that controls the printing of multiple small spots or pixels that are printed. The printed spots can be grouped or “clustered” to form print structures that are relatively stable for a given printing process. We refer to these clusters as “clustered-dots” or “dots”, and they are regularly spaced as determined by the size, shape, and tiling of the halftone cell. Conventional periodic halftone screens and halftone screen outputs can be considered as two-dimensional repeated patterns, possessing two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screens.

In this manner, a “digital screen” is created as an array of cells with pixels having threshold values. Each pixel has a set position and a set threshold value within the cell. Likewise, each cell has a set position within the digital screen. To create a halftone image, a contone image is broken down into an array of pixel-sized samples, and the gray level of each contone sample is stored. Next, each contone sample is compared with the halftone threshold value of the corresponding pixel in the halftone screen, and the pixel is darkened in the subsequent print image if the gray level of the contone sample is greater than the threshold value for that pixel. All the pixels of the digital screen are at set positions with respect to one another, such that a contone sample from the “top-left” of the picture would be compared with a pixel at the “top-left” of the digital screen. In other words, each digital screen pixel has a position which corresponds with and is associated with a position on the original contone picture.

Halftoning attempts to render images to printable form while avoiding unwanted visual texture, known as moiré, and tone reproduction irregularities. The two key aspects of halftone screen design are the geometry of periodic dot placement and the shape of the halftone dots. Controlling halftone dot shape has been a lower priority in laser printers because printer pixel resolution, typically measured in pixels per inch referring to the number of smallest printable spots per unit length, has been too low. Consider, for example, the task of controlling dot shape of a 212 cell per inch (cpi) 45° halftone screen used with a printer having a resolution of 600 pixels/inch, where the halftone cell is only two pixels in height, there are only few options to vary the shape of the halftone dot. As laser printing resolutions reach 2400 pixels/inch, and greater, controlling halftone dot shape provides a greater impact in improving a printed image.

As pixel resolution has increased with advancements in processor speed, memory capacity, printer and/or display capability, and the like, new options in halftone geometry have arisen. One area of development has been the so-called 2^(nd) generation stochastic screens, where nuclei (seeds) are placed in a stochastic manner (frequency modulated) up to a particular gray level, then the nuclei are grown in size (amplitude modulated) above that level.

Very little exists in the public domain literature on using 2^(nd) gen stochastic screen in any beneficial way for color printing. Most approaches simply overlay multiple screens, which can lead to an undesirable low spatial frequency correlation that could appear as coarse graininess. One such technique, described in U.S. Pat. No. 6,798,537, applies special processing for color printing using clustered halftone dots using vector error diffusion or multiple correlated halftone screens, without vector halftoning.

There is a need for systems and methods that employ dot-off-dot vector halftoning, providing improved stability of 2^(nd) generation stochastic screens over 1^(st) generation stochastic screens, and producing smoother textures and a larger gamut while using less ink compared to scalar halftoning while overcoming the aforementioned deficiencies.

BRIEF DESCRIPTION

In one aspect, a computer-implemented method for generating a halftone image using a parametrically controlled spot function on an irregular halftone grid comprises defining a 2^(nd) generation stochastic screen, performing vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image, and outputting the halftone image.

In another aspect, a system that facilitates generating a halftone image using a parametrically controlled spot function on an irregular halftone grid comprises a processor configured to define a 2^(nd) generation stochastic screen, perform vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image, and outputting the halftone image. The system further includes a printer that prints the halftone image.

In yet another aspect, a computer-implemented method for generating a halftone image using a parametrically controlled spot function and vector screening using a 2^(nd)-generation stochastic screen comprises defining a 2^(nd) generation stochastic screen, performing vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image, and outputting the halftone image. The method further includes, for an input pixel having a nonzero value for first and second colorants, defining multi-colorant level thresholds from the left end of the threshold vector for the first colorant, and defining multi-colorant level thresholds from a right end of the threshold vector for the second colorant. Additionally, the method includes, for an input pixel having a non-zero value for at least a third colorant, defining multi-colorant level thresholds form the middle of the threshold vector for the third colorant.

BRIEF DESCRIPTION OF THE DRAWINGS

The file of this patent contains at least one drawing executed in color. Copies of this patent with color drawing(s) will be provided by the U.S. Patent and Trademark Office upon request and payment of the necessary fee.

FIG. 1 illustrates a method of generating a halftone image by employing a parametrically controlled spot function, also known as a dot shape function, based on triangle tessellation and vector screening.

FIG. 2 shows an example of an array of input points or seeds that are defined as “activated” or “on”.

FIG. 3 shows an example of a triangle tessellation for a set of points, in accordance with one or more aspects described herein.

FIG. 4 illustrates a triangle having vertices P₁P₂P₃ and which encompasses a pixel P, in accordance with various aspects described herein.

FIG. 5 illustrates a vector of thresholds in ascending order, associated with an orthogonal distances to sides of spatially varying triangles, which are associated with (x, y) coordinates, such as may be used when applying a suitable type of vector screening algorithm using the spot function and given multi-colorant level information.

FIG. 6 illustrates an example of three-colorant dots growing from respective specified locations on a given triangle for a region of pixels having values defined by three colorant values.

FIG. 7 illustrates a schematic of the vector screening algorithm.

FIG. 8 illustrates several examples of the described technique applied to single colorant sweeps.

FIG. 9 illustrates several examples of 2-colorant sweeps.

FIG. 10 illustrates several examples of 3-colorant sweeps.

FIG. 11 illustrates an example of a 4-colorant halftone, which includes black, magenta, yellow, and cyan colorants.

FIG. 12 illustrates a system that facilitates generating a halftone image by employing a parametrically controlled spot function and a vector screening technique using a 2^(nd)-generation stochastic screen.

DETAILED DESCRIPTION

The above-described problem is solved by performing 2^(nd) generation vector stochastic halftoning. Vector screening or halftoning uses multiple colorants to make a halftone threshold decision. The described systems and methods employ a single stochastic screen defined up to a specified transition level. The dots at the specified level are connected to form a triangle tessellation with an associated spot function. For up to 3 colorants, the algorithm uses a vector screening method that is equivalent to a first colorant dot being grown from the vertices, second colorant dot grown from the triangle center, and a third colorant dot grown from the side midpoints. Growth in this manner ensures separation of colorants up to a certain density level. In cases where fourth colorant is to be used at a given pixel, the fourth colorant can be added using methods typically used for clustered screens, such as stochastic screening of the lightest colorant (i.e., the colorant having the highest L* value relative to the other colorants; the colorant having a color closest to white relative to the other colorants; etc.) in order to mitigate color shift sensitivity issues.

FIG. 1 illustrates a method of generating a halftone image by employing a parametrically controlled spot function, also known as a dot shape function, based on triangle tessellation and vector screening. The spot function is well suited for controlled growth of halftone spots arrayed on a non-regular grid as encountered in 2^(nd) generation stochastic screens. The herein-described spot function is general in that it can also be used for grids with regular order, such as conventional orthogonal halftones, hexagonally arrayed halftones, and general non-orthogonal halftones.

The method begins by defining a 2^(nd)-generation stochastic screen. At 10, a set of input points or “seeds” is received or generated from an initial source, such as a stochastic screen, or by randomly perturbing locations of seeds arranged in a regular grid, or the like. Stochastic screening is a halftone process that employs a pseudo-random distribution of halftone dots and uses frequency modulation (FM) to adjust dot density to achieve a desired gray level. At 12, a triangle tessellation is generated based on the seed locations. In one embodiment, triangle parameters, such as three heights or the like, are determined for each triangle. At 14, for each pixel, an “encompassing” triangle in which the pixel resides is determined or identified. At 16, each pixel's distance from its encompassing triangle's bases is determined. That is, the distance from each pixel to each base or side of its encompassing triangle is determined or calculated. At 18, calculated distances are input into a spot function on a pixel-by-pixel basis to determine output values that are used to generate halftone thresholds. At 20, a spot function value is output for each pixel. At this point the 2^(nd)-generation stochastic screen has been defined.

At 22, a vector screening technique is performed to threshold the image using the spot function(s) and given multi-colorant level information. The method can be employed to directly halftone an image or can be used to generate a sampled version of the spot function about a collection of seeds to yield a digital halftone cell that can be used to halftone an image.

It will be appreciated that the method of FIG. 1 can be implemented by a computer 30, which comprises a processor (such as the processor 204 of FIG. 11) that executes, and a memory (such as the memory 206 of FIG. 11) that stores, computer-executable instructions for providing the various functions, etc., described herein.

The computer 30 can be employed as one possible hardware configuration to support the systems and methods described herein. It is to be appreciated that although a standalone architecture is illustrated, that any suitable computing environment can be employed in accordance with the present embodiments. For example, computing architectures including, but not limited to, stand alone, multiprocessor, distributed, client/server, minicomputer, mainframe, supercomputer, digital and analog can be employed in accordance with the present embodiment.

The computer 30 can include a processing unit (see, e.g., FIG. 11), a system memory (see, e.g., FIG. 11), and a system bus (not shown) that couples various system components including the system memory to the processing unit. The processing unit can be any of various commercially available processors. Dual microprocessors and other multi-processor architectures also can be used as the processing unit.

The computer 30 typically includes at least some form of computer readable media. Computer readable media can be any available media that can be accessed by the computer. By way of example, and not limitation, computer readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data.

Communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of any of the above can also be included within the scope of computer readable media.

A user may enter commands and information into the computer through an input device (not shown) such as a keyboard, a pointing device, such as a mouse, stylus, voice input, or graphical tablet. The computer 30 can operate in a networked environment using logical and/or physical connections to one or more remote computers, such as a remote computer(s). The logical connections depicted include a local area network (LAN) and a wide area network (WAN). Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet.

FIG. 2 shows an example of an array 50 of input points or seeds 52 that are defined as “activated” or “on” such as may be received or generated at step 10 (FIG. 1) according to one or more features described herein. The seeds 52 are locations that define the nuclei for growth of the spot function. The seeds can be locations on a regular grid, or irregular locations as used for 2^(nd) generation stochastic screens. The seeds can be defined as activated (“on”) pixels on a pixel grid, or they can be represented as general spatial coordinates. In one embodiment, the seeds are generated as activated pixels using a stochastic screen halftone up to a target gray level, e.g., 15% area coverage or some other desired gray level, and the spot function grows each halftone dot about its respective seed. In optimizing the stochastic screen used for the seeds, a reduced range of frequency modulation (FM) use (e.g., 0 to 15% area coverage or some other desired range) can be employed, rather than for the full gray range as in conventional practices. When using the described method to generate a halftone cell, the cell can be treated as a hypertile so that seed distribution is not disturbed near the boundary.

FIG. 3 shows an example of a triangle tessellation 70 for a set of points as may be generated at step 12 (FIG. 1), in accordance with one or more aspects described herein. Given the seeds 52, a triangle tessellation is defined or generated based on seed locations. Triangle parameters, such as three heights, are determined for each triangle 72. According to one example, the pixel area that contains the seed locations is divided into triangles 72. The vertices of the triangles are the dot seeds 52. Every dot seed 52 is used as a vertex. By definition of a tessellation, the triangles completely fill the space and do not overlap. If the seeds form a particular periodic structure such as a hexagonal grid, then the tessellation would be regular and formed of congruent triangles. In the case of irregular grids, the tessellation would be irregular and formed of non-congruent triangles.

There are multiple options for forming the triangle tessellation. For example, a Delaunay triangulation algorithm or technique may be employed, in which a circumcircle of any triangle does not contain any other point. The Delaunay triangulation maximizes the minimum angle between vertices thereby avoiding skinny triangles. It may be employed for halftoning applications for that reason. Delaunay triangulation is the dual graph of the Voronoi tessellation, and the described method is naturally suited to operate using the dual Delaunay representation. Compared to any other triangulation of points, the smallest angle in the Delaunay triangulation is at least as large as the smallest angle in any other. However, the Delaunay triangulation does not necessarily minimize the maximum angle.

In another example, a greedy triangulation algorithm or technique is employed, which minimizes the total edge length of the resulting triangulation by adding the shortest internal diagonal to the triangulation at each step. According to another aspect, a polygon triangulation algorithm or technique is used, which decomposes the space into monotonic polygons that can be triangulated efficiently. In yet another example, a radial sweep algorithm or technique is employed, in which the central point of the set is connected to other points radially. Triangles are then formed by connecting radial edges together.

FIG. 4 illustrates a triangle 72 having vertices P₁P₂P₃ and which encompasses a pixel P such as is determined at step 14 (FIG. 1), in accordance with various aspects described herein. The triangle has heights H₁, H₂, and H₃, as well as pixel-intersecting heights h₁, h₂, and h₃. For a given pixel P, the triangle in which it resides is determined. Once encompassing triangles are defined, relatively straightforward geometric relationships can be used to determine useful triangle parameters, such as triangle heights H₁, H₂ and H₃, etc., as will be appreciated by those of skill in the relevant arts.

There are several contemplated options for determining or identifying the encompassing triangles. For instance, a crossing number technique or algorithm may be employed, which follows a ray that passes through the pixel and identifies the triangle whose sides intersect the ray twice, once on each side of the pixel P. According to another aspect, a winding number technique or algorithm is employed, which counts the number of times the triangle winds around the pixel. If the winding number is 0, the point is outside the triangle; otherwise, it is inside.

It will be appreciated that the step of determining encompassing triangles may optionally be omitted for seed points that lie on a pixel (e.g., “on” or “activated” pixels) rather than seed points that have a spatial coordinate not necessarily congruent with a pixel grid in which the pixels lie. That is, there is not a need to determine the encompassing triangle of a pixel if the pixel is located on a vertex of one or more triangle(s).

For each pixel, distances from its encompassing triangle vertices are determined, such as is discussed above with regard to step 16 of FIG. 1. The distances are determined from projections onto the triangle altitudes, or similarly, distances to the respective bases. An altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side. The length of the altitude is the height with respect to the given vertex. The opposite side is called the base of the altitude. The distances h₁, h₂ and h₃ are the distances from P to their respective bases, which are opposite P₁, P₂ and P₃ respectively. To implement a well-behaved (e.g., not fragmenting with controlled growth) spot function, the described method uses normalized heights (distances): h₁/H₁, h₂/H₂ and h₃/H₃, in accordance with various aspects.

The determined distances are employed to determine the value of a spot function that generates halftone thresholds. That is, the determined distances are input into the spot function, such as is discussed with regard to step 18 of FIG. 1. The spot function has parameters that can be adjusted to control its sharpness and slope. In one embodiment, the spot function is a weighted sum of three cosines that are functions of the three respective distances. Algebraic powers of the distances control sharpness of each dot touch point with its neighboring dots. Cosine weights control sequencing the touches, such that contact with neighboring dots can occur at different gray levels thereby avoiding instability that occurs for simultaneous touching. The spot function itself can be used to halftone an image, or a sampled version of the spot function can be applied as a threshold array for efficient implementation in a printer. Once all six distance values have been computed, the Q value of the pixel P is computed according to the following formula:

Q=a ₁ cos(π(2h ₁ /H ₁))+a ₂ cos(π(2h ₂ /H ₂))+a ₃ cos(π(2h ₃ /H ₁))   (1)

where a_(i) are parameters that control the elongation of the dot along the direction defined by H_(i). Note that since cosine is a symmetric function about π, the value of Q is the same regardless of whether the distances h_(i) are calculated with respect to a triangle side or to a line parallel to that side passing through the opposite vertex. For example, the value of Q would be the same if h′₁=H₁−h₁ is used instead of h₁.

If control over the roundness of the dot sides and the sharpness of corner touch points is desired, a new set of parameters γ_(i) can be introduced:

Q=a ₁ cos(π(2h ₁ /H ₁)^(γ) ¹ )+a ₂ cos(π(2h ₂ /H ₂)^(γ) ² )+a ₃ cos(π(2h ₃ /H ₁)^(γ) ³ )   (2)

Note that when γ_(i)≢0 for some i, the choice over how to measure h_(i) is no longer arbitrary since the symmetry of Q with respect to h_(i) is lost. In this case, the selection is constrained to be the distance between the point and whichever line is closest to it, be it the triangle side or its imaginary parallel replication passing through the opposite triangle vertex.

Another level of control can be enabled by inverting the spot function, such that:

Q=−(a ₁ cos(π(2h ₁ /H ₁)^(γ) ¹ )+a ₂ cos(π(2h ₂ /H ₂)^(γ) ² )+a ₃ cos(π(2h ₃ /H ₃)^(γ) ³ ))   (3)

The inversion allows for well controlled “holes,” which can be desirable for dark image subject matter.

According to another aspect, data normalization is an additional step that can be performed with spot functions. Once all pixels in the matrix are processed, the resulting entries are shifted and scaled to fit the data range, such as [0,255] for an 8-bit system or [0,1023] for a 10-bit image path.

According to related aspects, where the spot function has identical or nearly identical output values for multiple pixels in a dot, the order of the multiple pixels can be determined by any of a number of secondary criteria. For, instance a marking process or imager may mark pixels in a more consistent manner if pixels are preferentially added to a side, such as the lead edge, or trail edge of the dot as it moves through the process or start-of-scan or end-of-scan side of a dot relative to a laser imager scanning direction. For instance, angular considerations can be used to rank pixels. That is, to have minimal displacement of the centroid of the dot from gray level to gray level, pixels with nearly identical dot shape function values are sometimes selected by spiraling around the dot in quadrant (or hextant, etc.) steps. As another example, printed dot consistency is sometimes achieved by preferentially growing a dot in a vertical or horizontal direction where pixels having nearly identical spot function values are ranked to provide more growth in the preferred direction. In some cases, the fill order for pixels of nearly identical spot function values could be random, or selected by any of a number of other criteria.

FIG. 5 illustrates a vector 80 of thresholds in ascending order, associated with orthogonal distances to sides of spatially varying triangles, which are associated with (x, y) coordinates, such as may be used when applying a suitable type of vector screening algorithm using the spot function and given multi-colorant level information at 22 (FIG. 1). The halftone thresholding algorithm performed at 22 can be thought of as a form of vector screening method. For a given triangle, consider a vector of thresholds in numeric order where the value of each element is defined by the spot function. Each threshold t_(i) within a cell has been determined by the spot function value dependent upon an associated triplet of distances from the triangle sides (h₁,h₂,h₃)_(i). In conventional vector screening algorithms, the thresholds in the vector are determined by a pair of rectilinear coordinates within a rectangular cell based on simple modulo indexing into the cell, whereas the herein-described vector elements are associated with orthogonal distances to sides of spatially varying triangles that are determined from (x,y) points in space. For typical systems using 8, 9 or 10 bits per colorant per pixel, The maximum value of t_(N) would be 255, 511, or 1023, respectively.

FIG. 6 illustrates an example of three-colorant dots growing from respective specified locations on a given triangle 90 for a region of pixels having values defined by three colorant values. The three colors (magenta, cyan, and key or black) shown in the figure are provided by way of example for illustrative purposes and are not to be construed in a limiting sense. Here, the vector screening method performed at 22 is stated in a more algorithmic form. For a given input pixel f, having colorant values f=(f₁, f₂, f₃), halftoned pixel values p=(p₁, p₂, p₃) are determined. For a first nonzero colorant, apply t_(i) for its (h₁,h₂,h₃)_(i). If more than one colorant is nonzero, this threshold can be applied to the darkest (i.e., the colorant having a color closest to black, relative to the other colorants) or second darkest colorant. The first colorant k and its input value f_(k) and its halftoned value p_(k) are denoted as follows:

p_(k)=1 if f_(k)≧t_(i), else p _(k)=0   (Rule 1)

If a second colorant has a nonzero value, apply t_(N)−t_(i) for its (h₁,h₂,h₃)_(i). The first or second darkest colorant can be thresholded using this rule. The second colorant l and its input value f, and its halftoned value p_(l) is denoted as follows:

p _(l)=1 if f _(l) ≧t _(N) −t _(i), else p _(l)=0   (Rule 2)

If a third colorant has a nonzero value, apply ⊕t_(N/2)−t_(i)| for its (h₁,h₂,h₃)_(i). The lightest colorant can be thresholded using this rule. The third colorant m and its input value f_(m) and its halftoned value p_(m) is denoted as follows:

p _(m)=1 if f _(m) ≧|t _(i)|, else p _(m)=0   (Rule 3)

Rule 3 is optionally applied to the lightest colorant because the particular spot functions provided above have a least compact form for this rule, and therefore may print with less reliable density. This option may not be relevant for other spot functions.

FIG. 7 illustrates a schematic 96 of the vector screening algorithm employed at 22 (FIG. 1), which is different than vector screening methods used for 1^(st) gen stochastic screens. The schematic shows an order of thresholds used in the described vector screening technique. For a given input pixel the vector screening algorithm or technique performed at 22 is executed using multi-colorant level information in the following manner. For an input pixel having a nonzero value for only one colorant, multi-colorant level thresholds defined from the left of the vector are used. For an input pixel having a nonzero value for two colorants, multi-colorant level thresholds defined from the left of the vector for a first colorant, and from the right for the second colorant, are used. For an input pixel having a nonzero value for at least three colorants, multi-colorant level thresholds defined from the left of the vector for a first colorant, from the right for the second colorant, and the middle for the third colorant, are used.

As will be seen in the examples described with regard to FIGS. 8-11, the vector screening method produces dot-off-dot structure for the highlights, which produces smoother textures and a larger gamut while using less ink compared to scalar 2^(nd) gen halftoning. One potential problem that occurs with stochastic halftone screens is sensitivity to color shift with color-to-color misregistration. Some degree of “level blending” can be applied to alleviate this sensitivity. Level blending has been applied to 1^(st) gen vector halftoning to alleviate color shift sensitivity, but the method is very different for 2^(nd) generation stochastic halftone screens. For 1^(st) generation level blending, one threshold array is used and the fill order becomes more complicated. For example, for a second colorant, most of the fill uses the right of the threshold vector, while some smaller fraction uses the left to result in some dot-on-dot structure along with the primary dot-off-dot structure form from the right. In the described systems and methods, level blending is performed using slightly different spot functions for the different colorants. FIGS. 8-11 illustrate various examples of halftone images generated using the described parametrically controlled spot function and vector screening technique(s). The examples use an average dot-to-dot space of 14 pixels at 2400 spots per inch (spi), which is equivalent to 170 halftone cells per inch (cpi). In another example, 128 seeds are used within a 128×128 halftone cell.

FIG. 8 illustrates several examples of the described technique (FIG. 1) applied to single colorant sweeps. It will be noted that any single colorant used alone has a similar growth sequence. The Figure shows a black single colorant halftone 100, a magenta single colorant halftone 102, a cyan single colorant halftone 104, and a yellow single colorant halftone 106. In one example, different coefficients a_(i) can be used to generate slightly different thresholds for the different colorants while using the same triangle cellular structure. This technique involves generating three arrays using the spot function variations, one for each of the colorants. The thresholding rules are the same as described above, but a different set of thresholds is used for each colorant. The described technique reduces color-shift sensitivity by reducing the amount of dot-off-dot structure and introducing some dot-on-dot structure. A fourth colorant, when needed at a pixel, can be added using methods typically used for clustered screens, such as stochastic screening the lightest colorant.

FIG. 9 illustrates several examples of 2-colorant sweeps, including a black and cyan 2-colorant halftone 110, a magenta and cyan 2-colorant halftone 112, a yellow and cyan 2-colorant halftone 114, a black and magenta 2-colorant halftone 116, a magenta and yellow 2-colorant halftone 118, and a black and yellow 2-colorant halftone 120. It will be noted that the fills are dot-off-dot up to 50% area coverage. This dot-off-dot structure produces smoother textures and a larger gamut while using less ink compared to scalar halftoning. As previously mentioned, one potential problem is sensitivity to color shift with color-to-color misregistration. A degree of “level blending” can be built into the spot functions to alleviate this sensitivity.

FIG. 10 illustrates several examples of three-colorant sweeps, including: a black, magenta, and cyan 3-colorant halftone 130; a black, yellow, and cyan 3-colorant halftone 132; a black, magenta, and yellow 3-colorant halftone 134; and a yellow, magenta, and cyan 3-colorant halftone 136. It will be noted that the fills are dot-off-dot up to 33% area coverage. This dot-off-dot structure produces smoother textures and a larger gamut while using less ink compared to scalar halftoning. As previously mentioned, one potential problem is sensitivity to color shift with color-to-color misregistration. A degree of “level blending” can be built into the spot functions to alleviate this sensitivity.

FIG. 11 illustrates an example of a 4-colorant halftone 140, which includes black, magenta, yellow, and cyan colorants.

FIG. 12 illustrates a system 200 that facilitates generating a halftone image by employing a parametrically controlled spot function and a vector screening technique using a 2^(nd)-generation stochastic screen. The system comprises a print engine 202 that is coupled to a processor 204 that executes, and a memory 206 that stores computer-executable instructions for performing the various functions, methods, techniques, steps, and the like described herein. The processor 204 and memory 206 may be integral to each other or remote but operably coupled to each other. In another embodiment, the processor 204 and memory 206 are integral to the printer 202. In another embodiment, the processor and memory reside in a computer (e.g., the computer 30 of FIG. 1) that is operably coupled to the printer 202.

As stated above, the system 200 comprises the processor 204 that executes, and the memory 206 that stores one or more computer-executable modules (e.g., programs, computer-executable instructions, etc.) for performing the various functions, methods, procedures, etc., described herein. Additionally, “module,” as used herein, denotes a set of computer-executable instructions, software code, program, routine, or other computer-executable means for performing the described function, or the like, as will be understood by those of skill in the art. Additionally, or alternatively, one or more of the functions described with regard to the modules herein may be performed manually.

The memory may be a computer-readable medium on which a control program is stored, such as a disk, hard drive, or the like. Common forms of non-transitory computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, or any other magnetic storage medium, CD-ROM, DVD, or any other optical medium, RAM, ROM, PROM, EPROM, FLASH-EPROM, variants thereof, other memory chip or cartridge, or any other tangible medium from which the processor can read and execute. In this context, the systems described herein may be implemented on or as one or more general purpose computers, special purpose computer(s), a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA, Graphical card CPU (GPU), or PAL, or the like.

A set of input points or “seeds” 208 is received or generated from an initial source, such as a stochastic screen 209, or by randomly perturbing locations of seeds arranged in a regular grid, or the like, generated by the processor 204 from an input image scanned by the printing device 202, or from some other suitable source (i.e., the seeds need not come from an input image). The input points 208 and the stochastic screen are stored in the memory 206. The processor 204 executes a triangle tessellation module 210 to generate a triangle tessellation based on the seed locations. For instance, the input points or seeds 208 may be arranged in an irregular or non-uniform grid-like pattern, such as is shown in FIG. 2. The tessellation module 210 includes one or more of a Delaunay triangulation module 212. A greedy triangulation module 214, a polygon triangulation module 216, a radial sweep triangulation module 218, or any other suitable triangulation module.

For example, using the Delaunay triangulation module 212, a circumcircle of any triangle is constrained to pass through the three input point seeds forming the triangle without circumscribing any other point seed. The Delaunay triangulation maximizes the minimum angle between vertices thereby avoiding skinny triangles. In another example, the greedy triangulation module 214 is employed, which minimizes the total edge length of the resulting triangulation by adding the shortest internal diagonal to the triangulation at each step. According to another aspect, a polygon triangulation module 216 is executed, which decomposes the space into monotonic polygons that can be triangulated efficiently. In yet another example, a radial sweep module 218 is employed, in which the central point of the set is connected to other points radially. Triangles are then formed by connecting radial edges together.

The processor 204 executes an encompassing triangle identification module 220 that identifies “encompassing” triangles in which a pixel resides on a pixel-by-pixel basis. For instance, a crossing number module 222 can be executed, which follows a ray that passes through a given pixel and identifies the triangle whose sides intersect the ray twice, once on each side of the pixel P. According to another aspect, a winding number module 224 is executed, which counts the number of times the triangle winds around the pixel. If the winding number is 0, the point is outside the triangle; otherwise, it is inside.

The processor 204 executes a distance determination module 226 that determines or calculates each pixel's distance from its encompassing triangle's bases. That is, the distance from each pixel to each base or side of its encompassing triangle is determined or calculated. The distance determination module 226 also calculates or determines three heights for each triangle, including a height from each vertex to its opposite base or side. In this manner, six height or distance values are calculated: three pixel heights h₁, h₂, and h₃, and three triangle heights H₁, H₂, and H₃.

Once the six height values are determined for each pixel, the processor inputs the height values into a spot function (see, e.g., equations (1), (2), and/or (3) described with regard to the preceding Figures) on a pixel-by-pixel basis to determine output values that are used to generate halftone thresholds. In one example, the spot function is executed for each pixel as soon as the height values are available. In another example, the spot function is executed for all pixels once all pixels' height values have been determined. The processor 204 then executes a halftone module 230 that uses the spot function output values for each pixel, optionally with one or more secondary criteria or considerations, to halftone an image.

Additionally, the processor executes a vector screening module 231 that grows a first colorant dot from the vertices of a triangle in the tessellation, grows a second colorant dot the tessellation triangle center, and grows a third colorant dot grown from the side midpoints of the tessellation triangle. Growth in this manner ensures separation of colorants up to a predefined density level. To alleviate color shift sensitivity, a fourth colorant, when employed at a pixel, can be added using methods used for clustered screens, such as stochastic screening the lightest colorant using a stochastic screen 209. The vector screening module 231 comprises computer-executable instructions, which are executed by the processor 204, to perform the various functions, acts, techniques, etc., associated with step 22 of FIG. 1.

Image data 232 is stored in the memory 206 and may include input image data from which an input point seed grid is generated, intermediate image data that is generated at various points during the described process, output image data such as halftone image data that has been subjected to the vector screening module 231, etc. The output image data is provided to a print module 234 that, when executed by the processor 204, generates a set of commands or instructions that are executed by the processor 204 and/or the printer 202 to print the halftone image. In another embodiment, the output halftone image is displayed graphically on a graphical user interface 236 that may be integral to the printer 202, remote but operably coupled thereto, or may reside on a computer such as the computer 30 of FIG. 1. In this manner, the system 200 can be employed to directly halftone an image or can be used to generate a sampled version of the spot function about a collection of seeds to yield a digital halftone cell that can be used to halftone an image.

The exemplary embodiments have been described with reference to the preferred embodiments. Obviously, modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the exemplary embodiments be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof. 

1. A computer-implemented method for generating a halftone image using a parametrically controlled spot function on an irregular halftone grid, comprising: defining a 2^(nd) generation stochastic screen; performing vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image; and outputting the halftone image.
 2. The method according to claim 1, wherein the multi-colorant level information comprises: for an input pixel having a nonzero value for only one colorant, multi-colorant level thresholds that are defined from the left of a threshold vector; for an input pixel having a nonzero value for first and second colorants, multi-colorant level thresholds that are defined from the left end of the threshold vector for the first colorant, and multi-colorant level thresholds that are defined from a right end of the threshold vector for the second colorant; and for an input pixel having a nonzero value for at least three colorants, multi-colorant level thresholds that are defined from the left end of the threshold vector for the first colorant, multi-colorant level thresholds that are defined from the right end of the threshold vector for the second colorant, and multi-colorant level thresholds that are defined from the middle of the threshold vector for the third colorant.
 3. The method according to claim 1, wherein vector screening using the 2^(nd) generation stochastic screen comprises: for a given input pixel f, having colorant values f=(f₁, f₂, f₃), determining halftoned pixel values p=(p₁, p₂, p₃); for a first nonzero colorant, applying a threshold t_(i) for its respective heights (h₁,h₂,h₃)_(i). wherein if more than one colorant is nonzero, the threshold t_(i) is applied to the colorant having a color closest to black, relative to the other colorants
 4. The method according to claim 3, wherein a first colorant k and its input value f_(k) and its halftoned value p_(k) are denoted as: p _(k)=1 if f _(k) ≧t _(i), else p _(k)=0.   (Rule 1)
 5. The method according to claim 4, further comprising: if a second colorant has a nonzero value, applying a threshold t_(N)−t, for its respective heights (h₁,h₂,h₃)_(l); wherein the second colorant l and its input value f_(l) and its halftoned value p_(l) are denoted as: p _(l)=1 if f _(l) ≧t _(N) −t _(i), else p _(l)=0.   (Rule 2)
 6. The method according to claim 5, further comprising: if a third colorant has a nonzero value, applying a threshold |t_(N/2)−t_(i)| for its respective heights (h₁,h₂,h₃)_(l); the third colorant m and its input value f_(m) and its halftoned value p_(m) are denoted as: p _(m)=1 if f _(m) ≧|t _(N/2) −t _(i)|, else p _(m)=0.   (Rule 3)
 7. The method according to claim 1, further comprising performing a level blending technique on the 2^(nd) generation halftone screen, wherein a slightly different spot function is applied for each of a plurality of colorants.
 8. The method according to claim 1, further comprising: defining a set of input points arranged in an irregular grid; generating a triangle tessellation from the set of input points; identifying encompassing triangles, which each encompass at least one pixel; determining distances from a given pixel to each side of the encompassing triangle in which the pixel is located; for each pixel, executing the spot function using the determined distances to generate an output spot function value for each pixel; and employing the output spot function values when generating the halftone image.
 9. The method according to claim 8, wherein the triangle tessellation is generated using at least one of: a Delaunay triangulation algorithm; a greedy triangulation algorithm, which minimizes a total edge length of a resulting triangulation by adding a shortest internal diagonal to the triangulation at each step of the triangle tessellation generation; a polygon triangulation algorithm, which decomposes the irregular grid of input points into polygons that are subsequently triangulated; and a radial sweep algorithm in which input points are connected radially to neighbors iteratively until the triangle tessellation is complete.
 10. The method according to claim 8, wherein identifying encompassing triangles comprises at least one of: employing a crossing number algorithm that follows a ray that passes through the at least one pixel and identifies a triangle whose sides pass through the ray twice, once on each side of the at least one pixel; and employing a winding number algorithm that counts a number of times a triangle winds around the at least one pixel.
 11. A processor configured to execute computer-executable instructions for performing the method of claim 1, the instructions being stored on a computer-readable medium.
 12. A system that facilitates generating a halftone image using a parametrically controlled spot function on an irregular halftone grid, comprising: a processor configured to: define a 2^(nd) generation stochastic screen; perform vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image; and a printer that prints the halftone image.
 13. The system according to claim 12, wherein the multi-colorant level information comprises: for an input pixel having a nonzero value for only one colorant, multi-colorant level thresholds that are defined from the left of a threshold vector; for an input pixel having a nonzero value for first and second colorants, multi-colorant level thresholds that are defined from the left end of the threshold vector for the first colorant, and multi-colorant level thresholds that are defined from a right end of the threshold vector for the second colorant; and for an input pixel having a nonzero value for at least three colorants, multi-colorant level thresholds that are defined from the left end of the threshold vector for the first colorant, multi-colorant level thresholds that are defined from the right end of the threshold vector for the second colorant, and multi-colorant level thresholds that are defined from the middle of the threshold vector for the third colorant.
 14. The system according to claim 12, wherein the processor is configured to perform vector screening using the 2^(nd) generation stochastic screen by: for a given input pixel f, having colorant values f=(f₁, f₂, f₃), determining halftoned pixel values p=(p₁, p₂, p₃); for a first nonzero colorant, applying a threshold t_(i) for its respective heights (h₁,h₂,h₃)_(i). wherein if more than one colorant is nonzero, the threshold t_(i) is applied to the colorant having a color closest to black, relative to the other colorants
 15. The system according to claim 3, wherein a first colorant k and its input value f_(k) and its halftoned value p_(k) are denoted as: p_(k)=1 if f_(k)≧t_(i), else p_(k=)0.   (Rule 1)
 16. The system according to claim 15, wherein the processor is further configured to: if a second colorant has a nonzero value, apply a threshold t_(N)−t_(i) for its respective heights (h₁,h₂,h₃)_(l); wherein the second colorant l and its input value f and its halftoned value p_(l) are denoted as: p _(l)=1 if f _(l) ≧t _(N) −t _(i), else p _(l)=0.   (Rule 2)
 17. The system according to claim 16, wherein the processor is further configured to: if a third colorant has a nonzero value, apply a threshold |t_(N/2) −t _(i)| for its respective heights (h₁,h₂,h₃)_(l); wherein the third colorant m and its input value f_(m) and its halftoned value p_(m) are denoted as: p _(m)=1 if f _(m) ≧|t _(N/2) −t _(i)|, else p _(m)=0.   (Rule 3)
 18. The system according to claim 13, wherein the processor is further configured to perform a level blending technique on the 2^(nd) generation halftone screen, wherein a slightly different spot function is applied for each of a plurality of colorants.
 19. The system according to claim 12, wherein the processor is further configured to: define a set of input points arranged in an irregular grid; generate a triangle tessellation from the set of input points; identify encompassing triangles, which each encompass at least one pixel; determine distances from a given pixel to each side of the encompassing triangle in which the pixel is located; for each pixel, execute the spot function using the determined distances to generate an output spot function value for each pixel; and employ the output spot function values when generating the halftone image.
 20. The system according to claim 19, wherein the triangle tessellation is generated by the processor using at least one of: a Delaunay triangulation algorithm; a greedy triangulation algorithm, which minimizes a total edge length of a resulting triangulation by adding a shortest internal diagonal to the triangulation at each step of the triangle tessellation generation; a polygon triangulation algorithm, which decomposes the irregular grid of input points into polygons that are subsequently triangulated; and a radial sweep algorithm in which input points are connected radially to neighbors iteratively until the triangle tessellation is complete.
 21. The system according to claim 19, wherein the processor identifies encompassing triangles by at least one of: employing a crossing number algorithm that follows a ray that passes through the at least one pixel and identifies a triangle whose sides pass through the ray twice, once on each side of the at least one pixel; and employing a winding number algorithm that counts a number of times a triangle winds around the at least one pixel.
 22. A computer-implemented method for generating a halftone image using a parametrically controlled spot function and vector screening using a 2^(nd)-generation stochastic screen, comprising: defining a 2^(nd) generation stochastic screen; performing vector screening using the 2^(nd) generation stochastic screen with a spot function and multi-colorant level information to generate a halftone image; and outputting the halftone image; wherein for an input pixel having a nonzero value for first and second colorants, multi-colorant level thresholds that are defined from the left end of the threshold vector for the first colorant, and multi-colorant level thresholds that are defined from a right end of the threshold vector for the second colorant.
 23. The method according to claim 22, further comprising, for an input pixel having a nonzero value for at least a third colorant, defining multi-colorant level thresholds from the middle of the threshold vector for the third colorant.
 24. The method according to claim 23, further comprising, for an input pixel having a nonzero value for at least a fourth colorant, executing a stochastic screening technique on the lightest of the four colorants and identifying the remaining three colorants as the first, second, and third colorants prior to vector screening the input pixel. 